Gregory drew a rectangle ABCD on a coordinate plane. Point A is at (0,0). Point B is at (9,0). Point C is at (9,-9). Point D is at (0,-9). Find the length of side CD?

1 Answer
Neefgi
Mar 20, 2018

Side CD = 9 units

Explanation:

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If we ignore the y coordinates (the second value in each point), it's easy to tell that, since side CD starts at x = 9, and ends at x = 0, the absolute value is 9:

#| 0 - 9 | = 9#

Remember that the solutions to absolute values are always positive

If you don't understand why this is, you can also use the distance formula:

#P_"1"(9, -9)# and #P_"2"(0, -9)#

In the following equation, #P_"1"# is C and #P_"2"# is D:

#sqrt((x_"2"-x_"1")^2+(y_"2"-y_"1")^2#
#sqrt((0 - 9)^2 + (-9 - (-9))#
#sqrt((-9)^2 + (-9 + 9)^2#
#sqrt((81) + (0)#
#sqrt(81)=9#

Obviously that's the most detailed and algebraic explanation you could find, and is much more work than needed, but if you were wondering "why," that's why.

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